# Dynamics of charged elastic bodies under diffusion at large strains

## TL;DR

This paper develops a dynamic model for charged elastic and poroelastic bodies at large strains, incorporating electrostatic interactions and addressing non-self-interpenetration conditions to justify engineering assumptions.

## Contribution

It introduces a novel model combining Lagrangian and Eulerian descriptions for charged elastic bodies, accounting for large strains and electrostatic effects with partial non-self-interpenetration constraints.

## Key findings

- Model respects local non-self-interpenetration
- Handles large strains with electrostatic interactions
- Provides theoretical justification for engineering assumptions

## Abstract

We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope with possible global self-interpenetration, yielding thus a certain justification of most of engineering calculations which ignore these effects in the analysis of elastic structures. These models necessarily combine Lagrangian (material) description with Eulerian (actual) evolving configuration evolving in time. Dynamical problems are studied by adopting the concept of nonlocal nonsimple materials, applying the change of variables formula for Lipschitz-continuous mappings, and relying on the positivity of the determinant of the deformation gradient thanks to a result by Healey and Kroemer.